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The objective of this paper is to develop feasible gait patterns that could be used to control a real hexapod walking robot.These gaits should enable the fastest movement that is possible with the given robot?s mechanics and drives on a flatterrain. Biological inspirations are commonly used in the design of walking robots and their control algorithms. However,legged robots differ significantly from their biological counterparts. Hence we believe that gait patterns should be learnedusing the robot or its simulation model rather than copied from insect behaviour. ; However, as we have found tahula rasalearning ineffective in this case due to the large and complicated search space, we adopt a different strategy: in a seriesof simulations we show how a progressive reduction of the permissible search space for the leg movements leads to theevolution of effective gait patterns. This strategy enables the evolutionary algorithm to discover proper leg co-ordinationrules for a hexapod robot, using only simple dependencies between the states of the legs and a simple fitness function. ; Thedependencies used are inspired by typical insect behaviour, although we show that all the introduced rules emerge alsonaturally in the evolved gait patterns. Finally, the gaits evolved in simulations are shown to be effective in experiments ona real walking robot.